Mathematics, Ideas and the Physical Real

Author: Albert Lautman

Publisher: A&C Black

ISBN: 1441144331

Category: Philosophy

Page: 352

View: 475

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Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics. Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.

Mathematics and the Physical World

Author: Morris Kline

Publisher: Courier Corporation

ISBN: 0486136310

Category: Mathematics

Page: 512

View: 608

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Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

Essays on Deleuze

Author: Daniel W Smith

Publisher: Edinburgh University Press

ISBN: 0748655379

Category: Philosophy

Page: 480

View: 1687

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Brings together 18 key essays, plus two completely new essays, by one of the world's leading commentators on the work of the French philosopher Gilles Deleuze.

Badiou and Philosophy

Author: Sean Bowden

Publisher: Edinburgh University Press

ISBN: 0748668330

Category: Philosophy

Page: 288

View: 4594

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This collection of thirteen essays engages directly with the work of Alain Badiou, focusing specifically on the philosophical content of his work and the various connections he established with both his contemporaries and his philosophical heritage.

Synthetic Philosophy of Contemporary Mathematics

Author: Fernando Zalamea

Publisher: Urbanomic/Sequence Press

ISBN: 9780956775016

Category: Mathematics

Page: 385

View: 1274

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A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830-1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the "real mathematics" of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the "making of mathematics." In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.

The Mathematical Mechanic

Using Physical Reasoning to Solve Problems

Author: Mark Levi

Publisher: Princeton University Press

ISBN: 0691154562

Category: Science

Page: 186

View: 2900

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In this delightful book, Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can.

Are Numbers Real?

The Uncanny Relationship of Mathematics and the Physical World

Author: Brian Clegg

Publisher: St. Martin's Press

ISBN: 146689296X

Category: Mathematics

Page: 288

View: 4856

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Have you ever wondered what humans did before numbers existed? How they organized their lives, traded goods, or kept track of their treasures? What would your life be like without them? Numbers began as simple representations of everyday things, but mathematics rapidly took on a life of its own, occupying a parallel virtual world. In Are Numbers Real?, Brian Clegg explores the way that math has become more and more detached from reality, and yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity, to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader’s eyes to the hidden reality of the strange yet familiar entities that are numbers.

Teaching Mathematics in the Block

Author: Susan Nicodemus Gilkey,Carla Herndon Hunt

Publisher: Eye On Education

ISBN: 9781883001513

Category: Education

Page: 186

View: 5993

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Provides detailed instructional strategies, sample lesson plans, and sample assessments so that mathematics teachers can make the best use of the additional time.

What is Mathematics?

An Elementary Approach to Ideas and Methods

Author: Richard Courant,Herbert Robbins,Ian Stewart

Publisher: Oxford University Press, USA

ISBN: 9780195105193

Category: Mathematics

Page: 566

View: 1564

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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

Empiricism, Logic and Mathematics

Philosophical Papers

Author: Hans Hahn

Publisher: Springer Science & Business Media

ISBN: 9400989822

Category: Science

Page: 142

View: 1478

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The role Hans Hahn played in the Vienna Circle has not always been sufficiently appreciated. It was important in several ways. In the ftrst place, Hahn belonged to the trio of the original planners of the Circle. As students at the University of Vienna and throughout the fIrst decade of this century, he and his friends, Philipp Frank and Otto Neurath, met more or less regularly to discuss philosophical questions. When Hahn accepted his fIrSt professorial position, at the University of Czernowitz in the north east of the Austrian empire, and the paths of the three friends parted, they decided to continue such informal discussions at some future time - perhaps in a somewhat larger group and with the cooperation of a philosopher from the university. Various events delayed the execution of the project. Drafted into the Austrian army during the first world war" Hahn was wounded on the Italian front. Toward the end of the war he accepted an offer from the University of Bonn extended in recognition of his remarkable 1 mathematical achievements. He remained in Bonn until the spring of 1921 when he returm:d to Vienna and a chair of mathe matics at his alma mater. There, in 1922, the Mach-Boltzmann professorship for the philosophy of the inductive sciences became vacant by the death of Adolf Stohr; and Hahn saw a chance to realize his and his friends' old plan.

Mathematics and the Physical World

Author: Morris Kline

Publisher: Courier Corporation

ISBN: 0486136310

Category: Mathematics

Page: 512

View: 4702

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Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

Lost in Math

How Beauty Leads Physics Astray

Author: Sabine Hossenfelder

Publisher: Basic Books

ISBN: 0465094260

Category: Science

Page: 304

View: 9088

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A contrarian argues that modern physicists' obsession with beauty has given us wonderful math but bad science Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

Deleuze and the History of Mathematics

In Defense of the 'New'

Author: Simon Duffy

Publisher: A&C Black

ISBN: 1441113894

Category: Philosophy

Page: 208

View: 6998

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Gilles Deleuze's engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges are an opportunity to reconfigure particular philosophical problems - for example, the problem of individuation - and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze's philosophy, as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work. In the wake of Alain Badiou's recent and seemingly devastating attack on the way the relation between mathematics and philosophy is configured in Deleuze's work, Simon Duffy offers a robust defence of the structure of Deleuze's philosophy and, in particular, the adequacy of the mathematical problems used in its construction. By reconciling Badiou and Deleuze's seeming incompatible engagements with mathematics, Duffy succeeds in presenting a solid foundation for Deleuze's philosophy, rebuffing the recent challenges against it.

The Ideal and the Real

An Outline of Kant’s Theory of Space, Time and Mathematical Construction

Author: A. Winterbourne

Publisher: Springer Science & Business Media

ISBN: 9400914156

Category: Philosophy

Page: 139

View: 6430

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Many students coming to grips with Kant's philosophy are understandably daunted not only by the complexity and sheer difficulty of the man's writings, but almost equally by the amount of secondary literature available. A great deal of this seems to be - and not only on first reading - just about as difficult as the work it is meant to make more accessible. Any writer deliberately setting out to provide an authentically introductory text thus faces a double problem: how to provide an exegesis which would capture some of the spirit of the original, without gross and misleading over-simplification; and secondly, how to anchor the argument in the best and most imaginative secondary literature, yet avoid the whole project appearing so fragmented as to make the average book of chess openings seem positively austere. Until fairly recently, matters were made even more difficul t, in that commentaries on Kant were very often of a whole work, say, The Critique of Pure Reason, with the result that students would have to struggle through a very great deal of material indeed in order to feel any confidence at all that they had begun to understand the original writings. Recently, things have changed somewhat. There are now excellent commentaries on "Kant's Analytic", "Kant's Analogies" etc. . We have also seen, (at least as reflected in book titles), a resurgence of interest in what is perhaps the most controversial and far-reaching Kantian claim, viz.

MATHEMATICAL METHODS IN THE PHYSICAL SCIENCES, 3RD ED

Author: Boas

Publisher: John Wiley & Sons

ISBN: 9788126508105

Category: Mathematics

Page: 864

View: 5546

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Market_Desc: · Physicists and Engineers· Students in Physics and Engineering Special Features: · Covers everything from Linear Algebra, Calculus, Analysis, Probability and Statistics, to ODE, PDE, Transforms and more· Emphasizes intuition and computational abilities· Expands the material on DE and multiple integrals· Focuses on the applied side, exploring material that is relevant to physics and engineering· Explains each concept in clear, easy-to-understand steps About The Book: The book provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference. This book helps readers gain a solid foundation in the many areas of mathematical methods in order to achieve a basic competence in advanced physics, chemistry, and engineering.

The Oxford Book of Children's Verse in America

Author: Donald Hall

Publisher: Oxford Books of Verse

ISBN: 0195067614

Category: Juvenile Nonfiction

Page: 319

View: 796

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A collection of American poems written for children or traditionally enjoyed by children, by such authors as Longfellow, Poe, Eugene Field, Langston Hughes, Dr. Seuss, and Jack Prelutsky.

Mathematics in Western Culture

Author: Morris Kline

Publisher: Oxford University Press

ISBN: 9780195345452

Category: Mathematics

Page: 512

View: 4063

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This book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.

How People Learn

Brain, Mind, Experience, and School: Expanded Edition

Author: National Research Council,Division of Behavioral and Social Sciences and Education,Board on Behavioral, Cognitive, and Sensory Sciences,Committee on Developments in the Science of Learning with additional material from the Committee on Learning Research and Educational Practice

Publisher: National Academies Press

ISBN: 0309131979

Category: Education

Page: 384

View: 3384

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First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methods--to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education.